One way to discuss the theme of friendship in Julius Caesar is to look at statements of friendship versus actions of friendship.

Cassius makes many statements of friendship throughout the play, statements which contrast his ambitions. Antony, contrastingly, does not speak of friendship but instead speaks of honor. Though his own motives are debatable, Antony's actions suggest a real bond of loyalty to Caesar where Cassius' proclamations of affection ring false in light of his actions.

This is a big topic, and you might like to narrow it down to make your analysis more pointed and focussed. However, I will give you a few remarks to get you started as you gather your thoughts.

This play presents us with a world that is above all about the cut and thrust of politics, in every sense of these words. In this sense, friendship is a luxury that is often sacrificed in the face of political advantage and the desire for power. One of the most chilling examples of this is the way in which, in Act IV scene 1, Antony and Lepidus eerily mimic the conspirators earlier on in the play as they talk over who will be killed and who will survive in their own movement to gain power and control over Rome and the empire, before Antony turns very quickly on one of the Romans with whom he shares power:

This is a slight unmeritable man,

Meet to be sent on errands; is it fit,

The threefold world divided, he should stand

One of the three to share it?

Even though Antony has made a political alliance with Lepidus and Octavius, this "friendship" is shown to be based on nothing more than temporary convenience, and he is quick to challenge this alliance and suggest to Octavius that they should split the power between them alone rather than divide it three ways. Through such methods, Shakespeare presents us with a rather chilling impression of personal relations in this cloak-and-dagger world.